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Elsa陆艳 · 2022年03月12日

老师您好，中间步骤不太明白

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000242

问题如下：

Calculate the forward bucket 01s for a two-year bond with a coupon of 8% and a face value of USD 10,000 when the there are two buckets: 0–1 year and 1–2 year. Assume that the term structure is flat at 4% (semi-annually compounded).

选项：

解释：

The value of the bond is

400/1.02+400/1.022 +400/1.023 +10,400/1.024 = 10,761.5457

When the forward rates in the first bucket increase by one basis point, the value of the bond becomes

400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)= 10,760.5100

This is a decrease of 1.0358. When the forward rates in the second bucket increase by one basis point, the value of the bond becomes

400/1.02+400/1.022+400/(1.022×1.02005)

+10,400/(1.022×1.020052) = 10,760.5854

This is a decrease of 0.9604. The forward bucket 01s are therefore 1.0358 and 0.9604.

When the forward rates in the first bucket increase by one basis point, the value of the bond becomes

400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)= 10,760.5100

第三期和第四期的分母为什么是这样的？还有后面这一步也不太明白。

This is a decrease of 1.0358. When the forward rates in the second bucket increase by one basis point, the value of the bond becomes

400/1.02+400/1.022+400/(1.022×1.02005)

+10,400/(1.022×1.020052) = 10,760.585

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DD仔_品职助教 · 2022年03月13日

嗨，爱思考的PZer你好：


同学你好，

first bucket是0-1年的利率发生变化，1-2年没有，1-2年的第三笔和第四笔现金流进行折现的时候，会经过0-1这个区间，所以用0-1区间的利率折现，具体如下图：

second bucket就是1-2年的利率变化了，0-1年没有，和上面在折现时同理，一笔一笔往前折现要用当期时间段的利率，如下图：

最后一步就是在求价差，利率变化前后，价格的差值就是forward bucket01.

1.0357=10,761.5457-10,760.5100

0.9603=10,761.5457-10,760.5854

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NO.PZ2020011303000242问题如下Calculate the forwarbucket 01s for a two-yebonwith a coupon of 8% ana favalue of US10,000 when the there are two buckets: 0–1 yean1–2 year. Assume ththe term structure is fl4% (semi-annually compoun. The value of the bonis400/1.02+400/1.022 +400/1.023 +10,400/1.024 = 10,761.5457When the forwarrates in the first bucket increase one basis point, the value of the bonbecomes400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)= 10,760.5100This is a crease of 1.0358. When the forwarrates in the seconbucket increase one basis point, the value of the bonbecomes400/1.02+400/1.022+400/(1.022×1.02005)+10,400/(1.022×1.020052) = 10,760.5854This is a crease of 0.9604. The forwarbucket 01s are therefore 1.0358 an0.9604. 题目问2年期的债券couponrate是8%，面值是10k，当有2个buckets0-1年和1-2年时，计算forwarbucket 01s。假设利率的期限结构是flat，4%的利率，半年付息一次。债券价格= 400/1.02+400/1.022 +400/1.023 +10,400/1.024 = 10,761.5457当0-1年的bucket的forwarrate上升1bp时，债券价格变成= 400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)= 10,760.5100价格下降了1.0358. 当1-2年的bucket的forwarrate上升1bp时，债券价格变成=400/1.02+400/1.022+400/(1.022×1.02005)+10,400/(1.022×1.020052)= 10,760.5854价格下降了0.9604. The forwarbucket 01s 为 1.0358 和 0.9604. 我记得老师上课给我们讲过题的思路 然后说基本计算考的概率很低 所以不太需要掌握？

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